First Order Theory and Its Interpretation

Abstract

In this preparatory chapter, we present in a condensed manner the fundamental concepts and certain important results of first order predicate logic (FOPL) which we will use or reference in succeeding chapters. We have tried to state all definitions in a rigorous and self-contained manner, yet because of the limited space, we have omitted the proofs of theorems. Interested readers are referred to Shoenfield [Sho], Manna [Man] and Lloyd [Llo]. The word ‘logic’ is understood to mean the discourse that deals with a formal language, theories constructed in it and their interpretations. These are the respective subjects of the first three sections. Next, some of the major results on the undecidability and incompleteness of FOPL are summarized. The final section discusses a restriction of FOPL which is particularly relevant to computer science in that it forms the theoretical basis for theorem proving and logic programming.